Phase transition of an extrinsic curvature model on tori

TL;DR

This paper provides numerical evidence that a tethered surface model with extrinsic curvature experiences a first-order crumpling transition on triangulated tori, indicating a similar transition on compact surfaces.

Contribution

It demonstrates the first-order phase transition of the extrinsic curvature model specifically on tori, extending previous findings on spherical surfaces.

Findings

First-order crumpling transition observed on tori

Transition occurs between smooth and non-smooth phases

Supports the universality of the transition on compact surfaces

Abstract

We show a numerical evidence that a tethered surface model with extrinsic curvature undergoes a first-order crumpling transition between the smooth phase and a non-smooth phase on triangulated tori. The results obtained in this Letter together with the previous ones on spherical surfaces lead us to conclude that the tethered surface model undergoes a first-order transition on compact surfaces.